How can I enter this integral?

hm=1.5; 
t= 0:-0.1:-1;
m=100;
n=1:1:m;
Fs=zeros(length(t),length(n));
FEM=zeros(length(t),length(n));
for ii=1:length(t)
  for jj = 1:length(n);
    Lm=76.3-10*log10(hm);
    x=(-1j*t(ii)*sqrt(m-n)*sqrt(2/pi)+0.5);
    y=(exp(-t*srt(n-m)))/(sqrt(2j));
    S=int(sin(y),y=0..x);% how can I use this integration??
    C=int(cos(y),y=0..x);
    Fs(x)=y(S+1j*C);
    FEM(ii,jj)= (1/n)*sum(Lm(t(ii))*Fs);
  end
end

Answer 1

[Walter Roberson]

int() is used only for symbolic integration. You use integral() or older equivalents for numeric integration. integral() should be passed a function handle.

For example, to numerically integrate sin(t) over 0 to 2, one could use

integral(@(t) sin(t), 0, 2)

In your code you have a series of problems caused by using vectors. Your "n" is a vector, so sqrt(m-n) is going to be a vector so your x is going to be a vector and your y is going to be a vector. Then you try to integrate the vector sin(y) over y from 0 to x, but x is a vector and y has already been defined through a formula.

With you trying to use y as a variable of integration when y is defined by a formula, are you implicitly wanting to solve for the "t" such that the expression for y at that value of t gives you each value from 0 to x ?

If you have a fixed numeric vector of values, you would use trapz() or a similar integral approximation routine.

[sharif]

 Undefined function or method 'integral' for input arguments of type 'function_handle'.
S=integral(@(t)(sin(t^2)),0,x);

doesn't work

[Walter Roberson]

What MATLAB version are you using? integral() has been defined for a few releases now.

[sharif]

matlab 10 is the one i am using, I will first try to solve the integral problem and then I will try to solve the others, thanks for help

[Walter Roberson]

I believe integral() was introduced in R2011-something. Before that see quad() or quadgk()